Question

By what algebraic expression we need to divide x² +2x +1 to get x + 1 as quotient.​

Answer 1

Answer:

X + 1

Step-by-step explanation:

Answer 2

SOLUTION

TO DETERMINE

The algebraic expression we need to divide x² + 2x + 1 to get x + 1 as quotient

EVALUATION

We have to find the algebraic expression we need to divide x² + 2x + 1 to get x + 1 as quotient

Let R(x) be the required algebraic expression

Then by the given condition

$\displaystyle \sf{ \frac{ {x}^{2} + 2x + 1 }{R(x)} = x + 1 }$

Thus we get

$\displaystyle \sf{ R(x) = \frac{ {x}^{2} + 2x + 1 }{x + 1} }$

$\displaystyle \sf{ = \frac{ {x}^{2} + 2.x.1 + {1}^{2} }{x + 1} }$

$\displaystyle \sf{ = \frac{ {(x + 1)}^{2} }{x + 1} }$

$\displaystyle \sf{ = \frac{(x + 1)(x + 1) }{x + 1} }$

$\displaystyle \sf{ =x + 1 }$

FINAL ANSWER

The required algebraic expression = x + 1

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